The trio were leaving a restaurant in Alto do Lapa, Sao Paulo, on Wednesday night when they were snatched by the gang.
They were held for approximately 12 hours in which time the gang allegedly stole their car and money from their bank accounts before releasing them.
Model Luciana Curtis attends the Robert Geller fashion show during Mercedes-Benz Fashion Week Spring 2015
Getty
According to local reports, it was only the following morning that the alarm was raised by the couple's eldest child who found that her family had not returned home.
Curtis, who has worked with the likes of Beyoncé and featured on the covers of magazines like Cosmopolitan and Marie Claire, was reportedly held in a shack with her family overnight.
The family were eventually released by their captors as the police launched a search for the family. They eventually sought help from locals after their captors abandoned the hideaway, stealing the model's car.
They were quickly taken to safety and a spokesperson for the 47-year-old model confirmed the incident to local press saying: "The family has been released and they are safe and well."
Model Luciana Curtis
Getty
In a statement, police confirmed: "The armed criminals approached the victims outside a restaurant and took them captive. During the search by specialist police teams, the gang abandoned the family and fled."
Neither Luciana nor her husband have issued any comment themselves about the ordeal, reports The Sun.
Brazilian-born Curtis is the daughter of British businessman Malcolm Leo Curtis and teacher Katia Maria Furtado de Mendonca Curtis.
She was born in Sao Paulo but primarily lives in New York.
Curtis was also part of the worldwide campaign for L'Oreal's "True Match" powder and foundation with Beyoncé.
Earlier this year she featured alongside other models on the cover of ELLE Brazil.
The issue was an "ode to Brazilian supermodels who, from the late 1990s to the present day, have been taking the profession abroad, appearing on catwalks for major brands, and becoming muses of legendary stylists and established photographers".
